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infanta · 2023年05月17日

永续年金问题

  1. CFA I
  2. Quantitative

NO.PZ2018062016000012

问题如下：

David is going to retire in ABC company. The company has two retirement plans: Plan A is a one-time total retirement fund of $70,000, Plan B is a perpetuity of $900 at the end of each quarter that stated annual rate is 5% and compounded quarterly. Which plan should David choose?

选项：

A.

There is no difference

B.

Plan A

C.

Plan B

解释：

C is correct. The present value of Plan B is $900/(5%/4)=$72,000, which is larger than $70,000, the present value of Plan A. Therefore, David should choose Plan B.

永续年金的r为什么不是ear来计算

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星星_品职助教 · 2023年05月17日

同学你好，

永续年金的公式： PV=A/r 中，A和r的期间需要一致。

本题的付款频率是一季度一付（ $900 at the end of each quarter ），所以r必须也要是对应的季度利率。

如果题干中给出的付款频率是一年一付，此时r就需要转化为EAR。

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